JPH11240730A - Break cutting of brittle material - Google Patents

Abstract

PROBLEM TO BE SOLVED: To optimize the working conditions such as heating position and heating time and suppress the temperature increase at the heating spot in the break cutting of a strip plate with a point heat-source such as laser beam. SOLUTION: In the break cutting of a strip of a brittle material by heating the strip having a crack with a point heat source and propagating the crack by moving the heating spot, the working conditions are determined by setting at least one of the three parameters consisting of a dimensionless heating time (e.g. 4κt/W<2> ), a dimensionless length (e.g. D/W) and a dimensionless heating area (e.g. R/D or R/W) in such a manner as to maximize or nearly maximize a dimensionless stress expansion coefficient temperature ratio (e.g. 2K1 /αET(πW)<1/2> ) wherein (α) is linear expansion coefficient of the strip, (κ) is thermal diffusivity, (E) is longitudinal elastic modulus, (T) is temperature increase at the heating spot, (t) is heating time, (W) is half width of the strip, (R) is the radius of the heating area, (D) is the distance from the tip end of the crack to the heating center and (K1 ) is a stress expansion coefficient at the tip end of the crack.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for cutting brittle materials using thermal stress caused by a point heat source such as a laser.

[0002]

2. Description of the Related Art As a method of cutting a brittle material such as a semiconductor wafer, a ceramic substrate or a glass substrate, a crack is generated by a dicing method of grinding with a diamond blade or scribing using a roller chisel, a diamond point, or the like. Next, a scribing method in which a bending stress is applied to the crack to cut the crack is generally used. However, when cutting an electronic material on which a fine electronic circuit is formed, a conventional processing method cannot avoid generation of microcracks and particles, which may adversely affect products. As a countermeasure, for example, Japanese Unexamined Patent Publication No. 3-134040 discloses thermal stress cutting by a point heat source such as a laser. In this method, as shown in FIG. 16, a notch (initial crack) 22 is formed on the end face of a strip 21 made of a brittle material with a hard tool or the like, and then the vicinity 23 of the notch 22 is locally formed by a point heat source. Heating causes thermal stress distortion in the strip to cause the crack to grow, and thereafter, the point heat source is moved along the planned cutting line 24 to further develop the crack to cut the strip.

[0003]

A conventional method of cutting a strip by a point heat source such as a laser is to find the processing conditions such as the heating position and the heating time by trial and error every time the width or the material of the strip changes. Had been processed. Therefore, it is not easy to optimize the processing conditions, which requires a great deal of man-hours and increases the cost. This has been a factor that hinders automation of this type of laser processing apparatus. In addition, the temperature of the heating point becomes considerably high, especially in the case of small electronic components to be processed.
Temperature rise was remarkable, and important functions were sometimes impaired.

[0004] The present invention has been proposed in view of the above problems, and an object of the present invention is to easily optimize the processing conditions in the thermal stress cutting of a strip by a point heat source even if the width or the material of the strip changes. It is an object of the present invention to provide a new versatile method for cutting brittle materials, which is capable of improving the quality by appropriately suppressing the maximum temperature at the heating point.

[0005]

According to the method of the present invention for cutting a brittle material, the strip made of a brittle material having a crack is heated by a point heat source, the heating point is moved to cause the crack to grow, and the strip is cut. In the method of cleaving brittle material, the coefficient of linear expansion of the strip is α, the thermal diffusivity is κ, the longitudinal elastic modulus is E, the temperature at the heating point is T, the heating time is t, the half width of the strip is W, the area radius R, the distance from the crack tip to heat the center D, and the stress intensity factor of crack tip when the K _1, dimensionless stress intensity factor temperature ratio _{(e.g., 2K 1 / αET (πW)} 1/2 ) Is the maximum value or a value close to the maximum value, so that the dimensionless heating time (for example, 4 kt / W ² ) and the dimensionless distance (for example, D /
W), dimensionless heating area (eg, R / D or R / W)
The processing condition is determined by determining one or more of the three parameters consisting of: The above (πW) ^1/2 is the square root of πW (the same applies hereinafter).

In addition, 4κt / W ² ≦ 10 and R / D ≧
It is characterized by processing under conditions of 0.3 and 0.3 ≦ D / W ≦ 1.0.

[0007]

DESCRIPTION OF THE PREFERRED EMBODIMENTS The feature of the cleaving method of the present invention is that the vicinity of a crack tip of a strip made of a brittle material having an initial crack is locally heated by a point heat source such as a pulse laser and the heating point is moved. In the method of cleaving the strip by causing cracks to propagate, the coefficient of linear expansion of the strip is α, the thermal diffusivity is κ, the longitudinal elastic modulus is E, the temperature at the heating point is T, the heating time is t, and the strip is the half-width of the plate is W, the heating area radius R, the distance from the crack tip to heat the center D, and the stress intensity factor of crack tip when the K _1, dimensionless stress intensity factor temperature ratio (e.g., 2K ₁
/ ΑET (πW) ^1/2 ) becomes the maximum value or a value close to the maximum value so that the dimensionless heating time (for example, 4 kt /
W ² ), determining a processing condition by determining one or more of three parameters consisting of a dimensionless distance (for example, D / W) and a dimensionless heating region (for example, R / D or R / W). It is in. In particular, 4 kt / W ² ≦ 10 and R /
It is desirable to process under the condition of D ≧ 0.3 and 0.3 ≦ D / W ≦ 1.0.

[0008] Since all parameters are dimensionless, they can be applied irrespective of the geometrical conditions of the strip and the thermal and mechanical properties. Since this method is versatile, the processing conditions can be easily optimized even if the width and material of the strip change, and the maximum temperature at the heating point can be suppressed to the minimum necessary, resulting in lower cost and higher quality. Can be achieved. In particular, in order to obtain the strength of the stress singularity necessary for crack propagation at the lowest possible temperature rise, it is effective to actively expand the heating point and suppress the maximum temperature during strip processing. It is necessary to optimize the size, position, shape, etc. of the heating area. According to the present invention, the processing conditions can be optimized by determining the parameters so that the temperature ratio of the dimensionless stress intensity factor becomes the maximum value or a value close to the maximum value. The shape of the heating area is preferably a perfect circle, but a non-circular shape close to a perfect circle, a square,
Regular polygons such as regular pentagons, regular hexagons, regular octagons, and polygons close to these regular polygons may be shapes that can be regarded as approximately circular. As a specific brittle material, a semiconductor wafer, a ceramic substrate, a glass substrate, or the like is preferable.

Next, an analysis which is the basis of the cleaving method of the present invention will be described. First, we analyze the thermal stress field when the two heating sources are located at positions where the extension line of the crack is a symmetric line, and superimpose the solutions to obtain the center of the heating area with respect to the heating time for the target circular area heating. Evaluate the temperature rise of the part and the thermal stress intensity factor, examine how the thermal stress intensity factor / temperature rise changes with changes in the heating area, and determine the optimal area dimensions and area position where the value is maximized. To reveal. Furthermore, it will be explained that these analysis results agree well with the experimental results using the electronic material substrate.

(1) Thermal stress intensity factor at the time of two-point heating (1.1) Thermoelastic field generated by a point heat source of an infinite plate From time τ = 0 to τ = t, a thin infinite plate with initial temperature T = 0 is united Consider a temperature rise and a thermal stress distribution when heating is performed by a continuous point heat source having a heat quantity Q per unit thickness per unit time. When the plate thickness is sufficiently small, the temperature in the plate thickness direction is regarded as uniform, and the thermal stress field is in a plane stress state. If the heat radiation from the plate surface is ignored, the temperature field T ⁰ (r, t) and the thermal stress fields σ _r ⁰ (r, t), σΘ ⁰ (r, t) are given by the following equations.

(Equation 1)

(Equation 2)

(Equation 3) Where λ is the thermal conductivity, E is the longitudinal modulus, κ is the thermal diffusivity,
α is a coefficient of linear expansion, and the temperature field and the thermal stress field relate to polar coordinates (r, θ) with the heating point as the origin.

(1.2) Thermoelastic field generated by an infinite periodic point heat source acting on an infinite plate As shown in FIG. 1, a thin semi-infinite strip having a heat-insulating side wall having a width of 2 W and a crack length c is L from the left end face, and the center is The unsteady temperature field when heated by two point heat sources at a position 2 V away from the axis symmetric with respect to the axis is based on the principle of superposition, as shown in FIG.
It is expressed as the sum of the temperature fields due to various infinite periodic heat sources.
According to this solution, the temperature field of FIG.
2nW-V), (± L, ± 2nW + V), (n = 1, 2,
…) Are obtained by superimposing the temperature fields in the case of In addition, the thermal stress field of an infinite plate due to the two kinds of infinite periodic point heat sources is similar to the temperature field when the point heat source is (± L, ± 2 nW-V).
(± L, ± 2 nW + V) and (n = 1, 2,...) Are obtained by superimposing stress fields, and a temperature field T (x, y,
t), normal stress field σ _x (x, y, t), σ _y (x, y,
t) and the shear stress field τ _xy (x, y, t) are obtained as follows.

(Equation 4)

(Equation 5)

(Equation 6)

(Equation 7) here,

(Equation 8) And E ₁ (u) is the following integral exponential function:

(Equation 9)

The purpose of this analysis is to analyze the thermoelastic field around the crack tip at the beginning of heating, and the heat radiation from the plate surface is ignored because the heating time t is very short. Furthermore, it was assumed that the opening amount of the crack was small, and the temperature field of Expression (4) did not change with the opening of the crack surface.

(1.3) Analysis of Isothermal Stress Field The thermal stress field of an infinite flat plate generated by the two kinds of infinite periodic point heat sources corresponds to the case where a surface force acts on the end face of the strip, and the free surface Does not satisfy the conditions. In order to obtain a thermal stress field of a strip whose boundary is a free surface that is not subjected to a surface force, it is necessary to superpose an isothermal stress field of the strip that cancels the stress at the boundary. Incidentally, since cracks are not considered in the thermal stress field of an infinite flat plate, the stress intensity factor at the tip of a crack in a strip can be evaluated only by the isothermal stress field to be superimposed. For analysis of the isothermal stress field of the semi-infinite strip, a two-dimensional general-purpose analysis program by the body force method can be used. This analysis method is an optimal solution for a crack problem, and a highly accurate solution can be easily obtained. In the body force method, the boundary is discretized into several elements as in the normal boundary element method. The element division used here is shown in FIG.
At this time, the upper half of the semi-infinite strip was analyzed using the axial symmetry, and a linear element was used as the boundary. In the upper end surface, a range of 15 W is represented by a normal element, and the rest is represented by one semi-infinite element.

(1.4) Surface Force Along the End Surface The heating position was set to L = W in FIG. 1, and the distribution of the surface force to be superimposed on the boundary for various V / W values was calculated. FIG. 4 shows the results. The surface force to be superimposed on the upper end surface of the strip is tensile, and acts to open a crack. On the other hand, the stress σ _y generated by the two-point heating on the x-axis at the position to be a crack is compression, and the surface force superimposed to make the crack surface a free boundary acts in a direction to close the crack surface, Blocks the opening of cracks.

(1.5) Thermal Stress Intensity Factor When the crack length c is c / W> 5, the stress intensity factor generated in the strip by the point heat source hardly depends on the crack length.
Thus, a stress analysis was performed on a strip having an edge crack of c = 5 W subjected to the surface force described above, and a stress intensity factor K
₁ was evaluated as a function of heating time.

FIG. 5 shows the change over time of K ₁ obtained for various heating positions. Dimensionless time abscissa representing time and the vertical axis dimensionless a K ₁ in the heating quantity Q or the like. It had a significant K ₁ heating points from the figure closer to the center line, V
When / W exceeds 0.7, K ₁ is determined at the beginning of heating.
It turns out that becomes negative.

FIG. 6 shows isointensity lines obtained by connecting the heating positions giving the same magnitude of K ₁ by lines. The isointensity line of K ₁ = 0 is close to a triangle at the beginning of heating, and expands outward with time. If the area outside the iso-strength line is heated, K ₁ becomes negative at the crack tip, which is harmful to thermal stress cutting. Further, isointensity lines for K ₁ High levels close to a circle, goes slightly away from the crack tip over time.

(2) Thermal Stress Intensity Factor at the Time of Heating Circular Area Using the result at the time of two-point heating, a case of heating a circular area where the heating area spreads in a circular shape was analyzed. As shown in FIG. 7, the heating region is a circle having a radius R having a center on the extension line of the crack,
The distance from the crack tip to the center of the heating area is D, unit thickness,
The heating amount per unit area was set to Q _0. The heating area is divided into a small area ΔA = RdRdθ of Δθ = π / 50 in the angular direction and dR = D / 20 in the radial direction, and Q ₀ Δ is set at the center of ΔA.
Crack tip stress intensity factor ΔK ₁ with point heating source A
Then, the temperature rise ΔT at the center of the heating area was evaluated, and K ₁ , T at the time of heating the circular area was calculated by taking the sum of the entire heating area.

FIG. 8 shows the calculation result of the temperature rise at the center of the heating area when c / W = 5 and D / W = 1.0. The vertical axis is T
Is made dimensionless by the heating amount Q ₀ πR ² or the like. It can be seen that the temperature rise decreases as the heating region radius R increases, regardless of the heating time, and that it is effective to make the heating source wider to suppress the temperature rise. In addition, the temperature rises as the heating time increases.

FIG. 9 shows D / W = 0.3, 0.5,.
Shows the change to the size of the heating region of the stress intensity factor K ₁ at 0. Also vertical axis the figure is dimensionless and K ₁ in the heating amount Q ₀ .pi.R ² or the like. K ₁ regardless of the heating center position R / D
= 0, that is, at the time of the point heat source, and decreases as the R / D increases. This phenomenon becomes more remarkable as the heating time becomes longer. In the case where the heating time is short, even if the heating area is made larger, the influence on the decrease in K ₁ becomes smaller. Also, K ₁ increases with the increase of the heating time regardless of the heating center position and R / D.

(3) Temperature Ratio of Stress Intensity Factor when Heating Circular Region From the results of the temperature and the stress intensity factor when heating the circular region calculated in the previous section, the temperature ratio of stress intensity factor to temperature rise K ₁ /
T is required. The larger this value is, the lower the center temperature of the heating region, which is the highest attained temperature at the time of cutting, can be reduced.

FIG. 10 shows D / W = 0.3, 0.5, 1.0.
Shows the change of the stress intensity factor temperature ratio K ₁ / T with respect to the radius R of the heating region in FIG. In the case where the heating area was expanded to reach the crack tip (R = D), the stress intensity factor at R / D = 1 was considerably reduced from the maximum value in FIG. 9, but the temperature rise at that time was also small. The stress intensity factor temperature ratio K ₁ / T, which is their ratio, shows a maximum value or a value close to it at R / D = 1 as shown in FIG. The vertical axis in FIG.
^Since there is ^1/2, it can be seen that the narrower the sheet width, the higher the temperature at the time of cutting.

FIG. 11 shows the relationship between the radius of the heating area and the stress intensity factor temperature ratio K ₁ / T at which the temperature ratio K ₁ / T is at or near the maximum value.
The relation between K ₁ / T obtained when D is set and the heating position D is shown. When the heating time is shorter, K ₁ / T is larger, and when the heating time is 4κt / W ² = 0.1, the optimal heating region for suppressing the temperature rise and efficiently generating the stress intensity factor is R = D, It is near D / W = 0.7. D / W at which K ₁ / T becomes maximum as heating time 4κt / W ² increases
It can be seen that the optimum heating position approaches the crack tip.

As described above, when a strip-shaped substrate made of brittle material having an edge crack is cut by a point heat source, it is necessary to suppress the maximum temperature during processing from the viewpoint of quality. Because it is effective to have a spread,
For the basic circular area heating, the temperature rise at the center of the heating area with respect to the heating time and the thermal stress intensity factor are analyzed, and the thermal stress intensity factor / rising temperature (thermal stress intensity factor temperature ratio) K ₁ /
By paying attention to T, it was examined how this would change with changes in the heating area, and optimal conditions such as the heating position, heating area radius, and heating time that maximized K ₁ / T were calculated and determined. In addition, when the shape of the heating region is a non-circular shape close to a perfect circle, a square, a regular pentagon, a regular hexagon, a regular polygon such as a regular octagon, and a case close to these regular polygons, etc. It can be treated as the above-mentioned circular area heating. In this case, the radius of the heating area may be R, which is the radius of a circle circumscribing or inscribed in these shapes.

[0025]

EXAMPLE In order to verify the above analysis results, a point heat source 1 composed of an Nd: YAG laser in an arrangement as shown in FIG.
The cutting experiment of the strip 2 was performed using. At the end of the strip 1, a crack 3 is formed in advance on the center line. In addition,
The half width of the plate was W, the crack length was c, the distance from the crack tip to the heating center was D, and the radius of the heating area was R. Since the laser oscillator used had a large output, the output was adjusted by a diaphragm. In various processing conditions, and the lowest output Q _L required crack growth while increasing the laser output gradually, thermal damage was measured minimum output Q _U generated in the strip. Where Q _L and Q _U
Is the output without the stop. And locally margin of Q _U / Q _L Since it is difficult to measure the heating center temperature during cleaving, examine the change of the margin for the heating time, and to have been fractured by the larger the value of a low temperature. The relationship between Q _U / Q _L and K ₁ / T can be explained as follows.

As can be seen from FIG. 10, K ₁ / T is c /
When W and D / W are constant,

(Equation 10) It is expressed by the following relationship. Therefore,

[Equation 11] Becomes Further, since the T and Q are proportional, the amount of heating Q _L, Q _U
Assuming that the temperature rise at the time is T _L and T _U ,

(Equation 12) Becomes At this time, T _U coincides with the melting point T _{M of the} strip. Further, K ₁ generated at the time of T _L matches the fracture toughness value K _1c . From equations (10) to (12),

(Equation 13) Next, the change from _{Q U / Q L K 1 /} T can be confirmed experimentally. The used strips have a thickness of 0.1 mm and the pre-crack lengths are all c / W = 5. Table 1 shows the physical properties of the strip.

[0027]

[Table 1]

Next, the experimental results will be described. 2.2m width
m, D / W = 0.5 on a 15 mm long strip, 4 kt / W
Heating radius R at ² = 0.288 (heating time 2 ms)
13, FIG. 14 shows changes in Q _L and margin Q _U / Q _L for. From FIG. 13, it can be seen that as the heating radius R increases, the amount of heating required for cutting increases, and the stress intensity factor K ₁ is less likely to occur. However, as the heating radius increases, the minimum output Q _{U at} which thermal damage occurs also increases, so that Q _U / Q _L increases as R increases, contrary to the generation of K ₁ , as shown in FIG. Further, the value becomes maximum when R = D as in the analysis result.

Next, FIG. 15 shows a width of 1.2 mm and a length of 10 mm.
4κt / W ² = 0.969 (heating time 2 m
s), the margin Q _U / for the heating position D at R = D
The change in Q _L is shown. In this case, Q _U / D / W around 0.5
Q _L is maximized, it can be confirmed that agree well with the analytical results of 4κt / W ² = 1.0 shown in FIG. 11.

From the analysis results and experimental results described above,
Non-dimensional stress intensity factor temperature ratio (for example, 2K ₁ / αET
(ΠW) ^1/2 is the maximum value or a value close to the maximum value, the dimensionless heating time (for example, 4 kt / W ² ), the dimensionless distance (for example, D / W), the dimensionless heating region (for example, , R
/ D or R / W), it is possible to obtain suitable processing conditions by determining one or more of the three parameters. Practically, it is desirable to determine these parameters with reference to FIGS. At that time, 4kt / W
^{The value 2} is preferably as small as 10 or less, and at this time, the R / D is preferably as close to 1.0 as possible. D / W has an optimum value and varies depending on the value of 4κt / W ² , but is preferably about 0.3 or more and 1.0 or less.

[0031]

As described above, according to the method of the present invention for cutting a brittle material, a strip made of a brittle material having a crack is heated by a point heat source, and the heating point is moved to cause the crack to grow. In the method for cleaving a brittle material that cuts a plate, the coefficient of linear expansion of the band is α, the thermal diffusivity is κ, the longitudinal modulus is E, the temperature at which the heating point rises is T, the heating time is t, and the half width of the band is W, the heating area radius R, the distance from the crack tip to heat the center D, and the stress intensity factor of crack tip when the K _1, dimensionless stress intensity factor temperature ratio (e.g., 2K ₁ / αET (πW) ^1/2) is to a value close to the maximum value or the maximum value dimensionless heating time (e.g., 4κt / W ^2), the dimensionless distance (e.g., D /
W), dimensionless heating area (eg, R / D or R / W)
Since the processing conditions are determined by determining one or more of the three parameters consisting of, all the parameters are dimensionless and are independent of the geometrical conditions of the strip, thermal and mechanical properties. In addition, there is an unprecedented advantage that the maximum temperature at the heating point can be appropriately suppressed, and the cutting can be easily performed at a low temperature, thereby reducing costs and improving quality.

[Brief description of the drawings]

FIG. 1 is a diagram showing a breaking model of a semi-infinite strip by two-point heating.

FIG. 2 is a diagram showing a method of analyzing the unsteady temperature field of FIG. 1 based on the principle of superposition;

FIG. 3 is a diagram showing boundary element division for analyzing the isothermal stress field of a semi-infinite strip by the body force method.

FIG. 4 is a diagram showing a surface force distribution of an isothermal stress field on a boundary to be superimposed on a thermal stress field by a point heat source.

FIG. 5 is a diagram showing a change in a stress intensity factor at a crack tip with respect to a heating time.

FIG. 6 is a diagram showing a heating position at which the same magnitude of stress intensity factor is applied.

FIG. 7 is a diagram showing the cleavage of a semi-infinite strip having a crack by heating in a circular region.

FIG. 8 is a diagram showing a relationship between a heating area radius and a heating area center temperature at the time of heating a circular area.

FIG. 9 is a diagram showing the relationship between the size of the heating area and the stress intensity factor at the crack tip when heating the circular area.

FIG. 10 is a diagram showing the relationship between the size of the heating area and the temperature ratio of the stress intensity factor when heating the circular area.

FIG. 11 shows the relationship between the heating area radius and the stress intensity factor temperature ratio K ₁ /
Diagram showing the relationship between K ₁ / T and the heating position D obtained when T is set to R = D indicating the maximum value or a value close to

FIG. 12 is a diagram showing an outline of an experimental apparatus for cutting a strip using an Nd: YAG laser and each factor.

13 is a graph showing the relationship between the lowest laser output Q _L and the heating radius required crack growth

FIG. 14 is a diagram showing a relationship between a laser output margin capable of performing normal cutting and a heating radius.

FIG. 15 is a diagram showing a relationship between a laser output margin allowing normal cutting and a heating position.

FIG. 16 is a view for explaining conventional thermal stress cutting by a point heat source such as a laser.

[Explanation of symbols]

Reference Signs List 1 Nd: YAG laser (point heat source) 2 Semi-infinite strip 3 Crack 4 Protective film c Length of crack D Distance from crack tip to heating center R Heating zone radius W Half width of strip α Linear expansion coefficient κ Thermal diffusivity E longitudinal modulus T raised temperature t heating time K ₁ stress intensity factor

Claims (2)

[Claims] 1. A method for cleaving a strip made of a brittle material having a crack by heating the strip made of a brittle material with a point heat source, moving a heating point to cause a crack to progress, and cleaving the strip. Α, thermal diffusivity κ, longitudinal elasticity modulus E, heating temperature rise temperature T, heating time t, strip half width W, heating area radius R, distance from crack tip to heating center D, and the stress intensity factor of crack tip when the K _1, dimensionless stress intensity factor temperature ratio _{(e.g., 2K 1 / αET (πW)} 1/2) such that a value close to the maximum value or the maximum value Dimensionless heating time (eg, 4 kt / W ² ), dimensionless distance (eg, D /
W), dimensionless heating area (eg, R / D or R / W)
A method for cleaving a brittle material, wherein the processing condition is determined by determining one or more of three parameters consisting of: 2. The method according to claim 1, wherein 4 κt / W ² ≦ 10 and R / D ≧ 0.
3. The method for cutting a brittle material according to claim 1, wherein the working is performed under a condition of 0.3 and D / W ≦ 1.0.